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The general formulation of the boundary modulation technique is furnished. The strengths of the boundary element, the finite element and the analytical Fourier series methods have been integrated in a boundary method. The most generic problem of mathematical physics, that involves the Laplacian, is illustrated for arbitrary generalized convex domains. Specifically, a macro finite element is constructed analytically in the spirit of boundary elements. Instead of solving a set of simultaneous equations on a convex region, the orthogonality property of the test functions are employed on the transformed unit circle. The distributed forcing function is modulated by a factor which depicts the geometry of the physical domain. Applications to model the substructure deleter for seismic response calculations of embedded structures and the evaluation of the boundary element responses due to distributed forces motivated the formulation.
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